All-silicon raman amplifiers and laser based on micro ring resonators

ABSTRACT

Devices for generating a laser beam are disclosed. The devices include a silicon micro ring having at least one silicon optical waveguide disposed at a distance from the micro ring. The radius and the cross-sectional dimension of the micro ring, the cross-sectional dimension of the waveguide, and the distance between the micro ring and the waveguide are determined such that one or more pairs of whispering gallery mode resonant frequencies of the micro ring are separated by an optical phonon frequency of silicon. Methods of manufacturing a lasing device including a silicon micro ring coupled with a silicon waveguide are also disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent Ser. No. 13/196,674,filed Aug. 2, 2011, which is a continuation of U.S. patent Ser. No.12/392,634, filed Feb. 25, 2009, now U.S. Pat. No. 8,017,419, which is adivision of U.S. patent Ser. No. 11/354,725, filed Feb. 15, 2006, nowU.S. Pat. No. 7,532,656, which claims priority to U.S. ProvisionalApplication No. 60/653,556, filed Feb. 16, 2005.

FIELD

The present invention relates to optical amplification and lasingdevices, and methods for manufacturing the devices. More particularly,the present invention relates to low-threshold microcavity Raman lasers,and methods for manufacturing the same.

BACKGROUND

Stimulated Raman scattering (“SRS”) has a rich and evolving historysince the development of the laser. In 1962, SRS effect at infraredfrequencies was discovered. This discovery was soon described as atwo-photon process with a full quantum mechanical calculation. Toaccount for anti-Stokes generation and higher-order Raman effects,however, coupled-wave formalism was adopted to describe the stimulatedRaman effect. Self-focusing was later included to account for the muchlarger gain observed in SRS. These understandings facilitated the studyand design of Raman amplifiers and lasers. For example, low-thresholdmicrocavity Raman lasers have been demonstrated in silica micro spheresand micro disks using excited whispering gallery modes (“WGMs”). Suchdevices can play an important role in the developing technology ofphotonic integrated circuits.

Because silicon is being considered as a promising platform for photonicintegrated circuits, silicon based photonic devices have beenincreasingly researched. Microscopic passive silicon photonic devicessuch as bends, splitters, and filters have been developed. Activefunctionalities in highly integrated silicon devices have been studied,such as optical bistability due to the nonlinear thermal-optical effectand fast all-optical switching with two-photon absorption.

Silicon based Raman amplifiers and lasers also have been studied. Thebulk Raman gain coefficient g_(R) in silicon is 10⁴ times higher than insilica. Light generation and amplification in planar silicon waveguideswith Raman effects have been studied recently. Raman lasing using asilicon waveguide as the gain medium has been demonstrated, where thering laser cavity is formed by an 8-m-long optical fiber. A Raman laserusing an S-shaped 4.8-cm-long silicon waveguide cavity with multi-layercoatings has also been reported, which could be integrated ontoCMOS-compatible silicon chips.

Despite these advances, microscopic low-threshold Raman amplificationand lasing devices on a monolithic silicon chip has yet to be developed.Such devices would support the development towards efficient,all-optical photonic integrated circuits.

SUMMARY

Embodiments of the present invention provide all-optical on-chip signalamplification and lasing. In particular, embodiments of the presentinvention include Raman amplification and lasing devices using on-chipmicro ring resonators coupled with waveguides in monolithic silicon.Embodiments of the present invention also provide methods formanufacturing such devices. According to embodiments of the presentinvention, lasers are designed with geometries so that WGM resonantfrequencies of the micro ring resonator match the pump-Stokes frequencyspacing of SRS in monolithic silicon. Therefore, one or more pairs ofpump and Stokes light can form WGMs in the micro ring resonator.

Devices for generating a laser beam are disclosed. In some embodiments,the devices include a silicon micro ring having a radius and across-sectional dimension, and at least one silicon optical waveguidehaving a cross-sectional dimension and disposed at a distance from themicro ring. The distance, the radius, and the cross-sectional dimensionsare determined so that at least one pair of whispering gallery moderesonant frequencies of the micro ring are separated by an opticalphonon frequency of silicon.

Methods of manufacturing a lasing device including a silicon micro ringcoupled with a silicon waveguide are disclosed. In some embodiments, themethods include determining a radius and a cross-sectional dimension ofthe micro ring, a cross-sectional dimension of the waveguide, and adistance between the micro ring and the waveguide, so that at least onepair of whispering gallery mode resonant frequencies of the micro ringare separated by an optical phonon frequency of silicon. The methodsalso include manufacturing the lasing device by creating the micro ringwith the determined radius and cross-sectional dimension, creating thewaveguide with the determined cross-sectional dimension, and disposingthe micro ring from the waveguide at the determined distance.

BRIEF DESCRIPTION OF THE DRAWINGS

The Detailed Description of the Invention, including the description ofvarious embodiments of the invention, will be best understood when readin reference to the accompanying figures.

FIG. 1 a is a top view of a Raman amplification and lasing device inaccordance with various embodiments of the present invention.

FIG. 1 b is a cross-sectional view of the Raman amplification and lasingdevice in FIG. 1 a.

FIG. 2 is a transmission spectrum of a Raman amplification and lasingdevice according to one example of the present invention.

FIG. 3 is a diagram illustrating the WGMs formed by a beam of light inthe same example device as used for FIG. 2.

FIG. 4 is a diagram illustrating the WGMs formed by another beam oflight in the same example device as used for FIG. 2.

FIG. 5 is a flow chart illustrating methods for manufacturing a Ramanamplification and lasing device according to various embodiments of thepresent invention.

FIG. 6 is a top view of a fabricated Raman amplification and lasingdevice according to various embodiments of the present invention.

DETAILED DESCRIPTION

Devices of various embodiments of the present invention use micro ringresonators as a cavity for producing Raman laser. The strong lightconfinement of a micro ring resonator enhances the stimulated Ramanscattering with low-threshold pump power.

FIG. 1 a is a top view and FIG. 1 b is a cross-sectional view of a Ramanamplification and lasing device of various embodiments of the presentinvention, generally at 100. Device 100 includes an optical micro ringresonator 102 and an optical waveguide 104, both made of silicon. Thecross-sectional view illustrates a cross section of device 100 taken bya plane perpendicular to the sheet and passing through the center ofmicro ring resonator 102.

In some embodiments, waveguide 104 can be a quasi-transverse electric(“quasi-TE”) single-mode waveguide. As shown, micro ring resonator 102has radius R. Micro ring resonator 102 and waveguide 104 can have thesame width w and height t_(si). There is a gap s between resonator 102and waveguide 104. Resonator 102 and waveguide 104 can be formed on topof a layer of silicon oxide (SiO₂) 106. In some embodiments, device 100can include more than one waveguide disposed at a close distance toresonator 102. Although waveguide 104 is shown to be straight in FIG. 1,it can assume other shapes as known in the art.

In operation, pump light can enter the lower end 109 of waveguide 104 inthe direction of arrow 108. This pump light can induce pump light inresonator 102 in the direction of arrow 110 by a coupling effect. Whenresonator 102 is stimulated, Stokes light in resonator 102 is generatedby Raman scattering, which causes Stokes light leaving the upper end ofwaveguide 104 by the coupling effect.

Stimulated Raman scattering in micro ring resonator 102 is a two-photonprocess related to the optical phonons. The strongest Stokes peak arisesfrom single first-order Raman-phonon (three-fold degenerate) at theBrillouin zone center. The coupling between the pump and Stokeslightwaves in SRS can be described by Maxwell's equations usingnonlinear polarizations P⁽³⁾:

$\begin{matrix}{{{\nabla{\times \left( {\nabla{\times E_{s}}} \right)}} + {\frac{1}{c^{2}}\frac{\partial^{2}}{\partial t^{2}}\left( {ɛ_{s}E_{s}} \right)}} = {{- \frac{1}{c^{2}}}\frac{\partial^{2}}{\partial t^{2}}\left( P_{s}^{(3)} \right)}} & (1) \\{{{\nabla{\times \left( {\nabla{\times E_{p}}} \right)}} + {\frac{1}{c^{2}}\frac{\partial^{2}}{\partial t^{2}}\left( {ɛ_{p}E_{p}} \right)}} = {{- \frac{1}{c^{2}}}\frac{\partial^{2}}{\partial t^{2}}\left( P_{p}^{(3)} \right)}} & (2)\end{matrix}$

The nonlinear polarization P_(S) ⁽³⁾ is cast as χ_(jkmn)⁽³⁾E_(p)E_(p)*E_(s), where χ_(jkmn) ⁽³⁾ is the third-order fourth-rankRaman susceptibility, and can be calculated in terms of the Raman tensorR _(i). The E_(p) and the E_(s), are electric fields of the pump andStokes waves respectively.

In micro ring resonator 102, it can be shown that the cavity SRSenhancement results from the intensity build up in the cavity, so thatthe threshold pump power depends on the quality factor Q and also thecoupling efficiencies. The intensity build up factor for the cavity modeis:

I _(c) /I ₀=(Qλ)/(π² nR)  (3)

where I₀ is the intensity of the input light, I_(c) is the effectiveintensity of the light in the cavity, λ is the light wavelength, n isthe refraction index of the micro ring resonator 102 host material, andR is the radius of the micro ring resonator 102. The effectiveinteraction length is:

L _(c)=(Qλ)/(2πn)  (4)

Both pump mode and Stokes mode can be WGMs with quality factors Q_(p)and Q_(s), respectively. The condition for Raman lasing is that the gainexceeds the losses:

g _(R) ξI _(c,pump) >L _(c,Stokes) ⁻¹  (5)

Assume that the modal volume is V_(m)≈2πRA, the threshold pump powerP_(th)=I₀A is:

$\begin{matrix}{P_{th} = {\frac{\pi^{2}n^{2}}{\xi \; g_{R}Q_{s}Q_{p}}\frac{V_{m}}{\lambda_{p}\lambda_{s}}}} & (6)\end{matrix}$

where the parameter ξ<1 describes the coupling to the pump mode and theoverlap between the pump and Stokes modes, A is the effectivecross-sectional area of the cavity mode, and g_(R) is the bulk Ramangain coefficient of silicon, which is about 70 cm/GW for Stokesradiation in the 1550-nm range.

Because the quality factors Q_(s) and Q_(p) of pump mode and Stokes modeare relatively high, threshold power P_(th) can be made very low.Therefore, by designing a highly confined micro ring resonator 102 thatsupports pump and Stokes modes, a microscopic low-threshold on-chipamplification and lasing device 100 can be fabricated.

The following describes the design of device 100 that supports one ormore pump and Stokes modes. Device 100 can be designed by numericallysolving Maxwell's equations (1) and (2) with a boundary conditioncorresponding to the geometry of device 100, using a three-dimensionalfinite-difference time-domain (3D FDTD) method. With a 3D FDTD method, atransmission spectrum of device 100, resonant wavelengths, WGM fieldprofiles, and quality factor Q of the resonant wavelengths can all becalculated. This can be performed with any software that numericallysolves the Maxwell's equations (1) and (2), such as the FullWAVE™software provided by RSoft Design Group, Inc. (Ossining, N.Y.).

An important goal of the design is to determine iteratively (i.e.,fine-tune) the geometry of device 100 so that WGM resonant frequenciesof micro ring resonator 102 corresponds to one or more pairs of pump andStokes frequencies. A pump frequency and a corresponding Stokesfrequency are spaced apart by Δ_(v)=15.6 THz, which is the opticalphonon frequency in monolithic silicon. If a pair of WGM resonantfrequencies are separated by 15.6 THz, a pump light having one of thepair of frequencies can be used to generate a Stokes light having theother frequency, and both the pump and the Stokes light can form WGMs inresonator 102.

If it is desirable that device 100 supports pump and Stokes lights withwavelengths close to a predetermined wavelength (e.g., 1550 nm), thegeometry of device 100 can be determined iteratively so that wavelengthscorresponding to the WGM resonant frequencies of resonator 102 are closeto the predetermined wavelength (e.g., within the range of about 1400 nmto about 1600 nm). However, device 100 is not limited by the exampleprovided; device 100 can also be designed to support pump and Stokeslights with wavelengths within other suitable ranges.

According to various embodiments of the present invention, a numericaldesign process can include determine iteratively the geometry of device100 and calculating the corresponding transmission spectrum of waveguide104 with, for example, a 3D FDTD method. The drops in the transmissionspectrum correspond to WGM resonant frequencies of resonator 102. Fromthe transmission spectrum, a pump wavelength λ_(p) can be chosen, suchthat λ_(p) corresponds to a drop in the transmission spectrum. Then, theStokes wavelength can be calculated with λ_(s)=λ_(p)+λ_(p)²/(c/Δv−λ_(p)). Stokes wavelength λ_(s) should also correspond to a dropin the transmission spectrum. Quality factors Q_(p) and Q_(s) can thenbe calculated with Q=λ/Δλ_(FWHM) from the transmission spectrum.

Determining iteratively the geometry of device 100 can includedetermining iteratively the radius R of resonator 102, the width w andthe height t_(Si) of waveguide 104 and micro ring resonator 102, and thegap s between waveguide 104 and resonator 102, so that the transmissionspectrum of waveguide 104 have certain desired properties. For example,width w and height t_(Si) can be changed it to shift the high Q resonantspectrum of device 100 to a range close to 1550 nm. A starting point forthe iterative determination of width w and height t_(Si) can be valuesthat support a quasi-TE single-mode waveguide 104. Radius R can bedetermined iteratively so that optical phonon frequency (15.6 THz) is aninteger multiple of the free spectral range, which is the spacingbetween the neighboring WGM resonant frequencies of resonator 102 (theWGM resonant frequencies corresponds to drops in the transmissionspectrum of the waveguide). Gap s can be determined iteratively toachieve a good electromagnetic coupling efficiency into and out ofresonator 102 for different wavelength ranges.

As an example, device 100 can be designed with w equals to 350 nm,t_(Si) equals to 200 nm, s equals to 150 nm, and R equals to 4.9 μm. Inthis example, the cross-sectional dimension of waveguide 104 asrepresented by w and t_(Si) supports a quasi-TE single-mode. Heightt_(oxide) of SiO₂ layer 106 can be 400 nm. The refraction index ofsilicon and SiO₂ can be n_(Si)=3.48 and n_(oxide)=1.46 respectively.

FIG. 2 illustrates the quasi-TE transmission spectrum near 1550 nm ofwaveguide 104 coupled with resonator 102 according to this exampledesign. As shown, two pump lights (Pump 1 and Pump 2) can be selectedfrom the transmission spectrum, with wavelengths λ_(p1)=1431.8 nm andλ_(S1)=1546.5 nm. Two corresponding Stokes lights (Stokes 1 and Stokes2) have wavelengths λ_(p2)=1444.8 nm and λ_(S2)=1562.5 nm, which alsocorrespond to drops of the transmission spectrum.

FIG. 3 illustrates the WGMs of Pump 1 inside micro ring resonator 102 ofthis example with continuous wave excitation. The white dots 302 inresonator 102 are the locations having stronger Hy field (magnetic fieldin the Y direction). It can be seen that Pump 1 forms WGMs in resonator102. The WGMs of Pump 1 in resonator 102 are caused by Pump 1 inwaveguide 104 traveling in the direction of arrow 108 (Z direction).

FIG. 4 illustrates the WGMs of Stokes 1 inside micro ring resonator 102of this example with continuous wave excitation. The white dots 402 inresonator 102 are the locations having stronger Hy field (magnetic fieldin the Y direction). It can be seen that Stokes 1 forms WGMs inresonator 102 as well. The WGMs of Stokes 1 in resonator 102 are causedby Stokes 1 in waveguide 104 traveling in the direction of arrow 108 (Zdirection).

Therefore, device 100, according to the example design, supports theWGMs of both Pump 1 and Stokes 1. By SRS and coupling, Pump 1 inwaveguide 104 can induce WGMs of both Pump 1 and Stokes 1 in micro ringresonator 102, and hence Stokes 1 in waveguide 104. Similarly, device100, according to the example design, supports the WGMs of both Pump 2and Stokes 2. It should be noted that the example geometry of device 100is not the only geometry that can support WGMs of the required pump andStokes frequencies.

FIG. 5 is a flow chart illustrating various processes for manufacturingRaman amplification and lasing devices of various embodiments of thepresent invention. At 500, a suitable geometry of device 100 isdetermined. At 502, a layer of polymethylmethacrylate (“PMMA”) can becoated on top of a silicon-on-insulator (“SOT”) wafer. For example, a200 nm thick 495 495K A6 PMMA can be spin-coated on top of a SOI wafer.At 504, a design pattern according to the determined geometry can bewritten on the PMMA layer by electron-beam lithography. At 506, theexposed PMMA layer can be developed in a solution. For example, asolution of methylbutylisoketone (“MIBK”) and isopropyl alcohol (“IPA”)with MIBK:IPA=1:3 can be used to develop the PMMA layer for about 55seconds. At 508, a chrome mask can be transferred on top of the SOIwafer by thermal evaporation. At 510, the SOI wafer can be etched toform the designs in the wafer, using, for example, inductively coupledplasma (“ICP”) etching. At 512, the chrome mask can be removed. Thewafer can be further packaged to seal the optical devices fabricated onthe wafer. FIG. 6 is a top view of a fabricated Raman amplification andlasing device of various embodiments of the present invention capturedby scanning electron microscopy (“SEM”).

Each of the following applications, publications and patents are herebyincorporated by reference in their entirety: U.S. patent applicationSer. No. 13/196,674, filed Aug. 2, 2011, published as U.S. 2011/0286489;U.S. patent application Ser. No. 12/392,634, filed Feb. 25, 2009,published as U.S. 2009/0191657, now U.S. Pat. No. 8,017,419; U.S. patentapplication Ser. No. 11/354,725, filed Feb. 15, 2006, published as U.S.2007/0025409, now U.S. Pat. No. 7,532,656; and Provisional ApplicationNo. 60/653,556, filed Feb. 16, 2005.

Other embodiments, extensions, and modifications of the ideas presentedabove are comprehended and within the reach of one skilled in the artupon reviewing the present disclosure. Accordingly, the scope of thepresent invention in its various aspects should not be limited by theexamples and embodiments presented above. The individual aspects of thepresent invention, and the entirety of the invention should be regardedso as to allow for modifications and future developments within thescope of the present disclosure. The present invention is limited onlyby the claims that follow.

1. A configuration for providing an electro-magnetic radiation, comprising: a ring arrangement having an interior dimension and at least one portion with a first cross-sectional dimension; and at least one silicon waveguide arrangement having at least one portion with a second cross-sectional dimension, the waveguide disposed at a distance from the ring arrangement, wherein at least one of the distance, the interior dimension, the first cross-sectional dimension, and the second cross-sectional dimension having values such that, during operation of the configuration, at least one first whispering gallery mode resonant frequency of the ring arrangement and at least one second whispering gallery mode resonant frequency of the ring arrangement are separated from one another based on an optical phonon frequency of silicon.
 2. The configuration according to claim 1, wherein the electro-magnetic radiation includes a laser beam.
 3. The configuration according to claim 1, wherein the ring arrangement comprises a silicon micro-ring.
 4. The configuration according to claim 1, wherein the first and second whispering gallery mode resonant frequencies are separated from one another by the optical phonon frequency of silicon.
 5. The configuration according to claim 1, wherein the first cross-sectional dimension approximately corresponds to the second cross-sectional dimension.
 6. The configuration according to claim 1, wherein, during the operation of the configuration, wavelengths corresponding to at least one of the at least one first whispering gallery mode resonant frequency or the at least one second whispering gallery mode resonant frequency are within a range of about 1400 nanometers to about 1600 nanometers.
 7. The configuration according to claim 1, wherein the at least one waveguide arrangement includes a single-mode waveguide.
 8. The configuration according to claim 1, wherein the at least one waveguide arrangement includes a quasi-transverse electric single-mode waveguide.
 9. The configuration according to claim 1, wherein, during the operation, the at least one waveguide arrangement has a transmission spectrum with a plurality of drops.
 10. The configuration according to claim 9, wherein neighboring ones of the drops are separated from one another by a free spectral range.
 11. The configuration according to claim 10, wherein an optical phonon frequency of monolithic silicon approximately equals to an integer multiplied by the free spectral range.
 12. The configuration according to claim 1, wherein at least one of the distance, the interior dimension, the first cross-sectional dimension, or the second cross-sectional dimension are provided based on a corresponding transmission spectrum of the waveguide which has a first drop at a pump frequency and a second drop at a Stokes frequency.
 13. The configuration according to claim 12, wherein the pump frequency and the Stokes frequency differ from one another by the optical phonon frequency.
 14. The configuration according to claim 1, further comprising at least one layer on which the ring arrangement and the at least one silicon waveguide arrangement are provided.
 15. The configuration according to claim 14, wherein the at least one layer comprises at least one polymethylmethacrylate layer.
 16. A method of facilitating a configuration for generating an electro-magnetic radiation, comprising: providing a ring arrangement having an interior dimension and at least one portion with a first cross-sectional dimension; providing at least one silicon waveguide arrangement having at least one portion with a second cross-sectional dimension; and disposing the waveguide at a predetermined distance from the ring arrangement, wherein at least one of the distance, the interior dimension, the first cross-sectional dimension, and the second cross-sectional dimension having values such that, during operation of the configuration, at least one first whispering gallery mode resonant frequency of the ring arrangement and at least one second whispering gallery mode resonant frequency of the ring arrangement are separated from one another based on an optical phonon frequency of silicon.
 17. The method according to claim 16, wherein the electro-magnetic radiation includes a laser beam.
 18. The method according to claim 16, wherein the ring arrangement comprises a silicon micro-ring.
 19. The method according to claim 16, wherein the first and second whispering gallery mode resonant frequencies are separated from one another by the optical phonon frequency of silicon.
 20. The method according to claim 16, wherein the first cross-sectional dimension approximately corresponds to the second cross-sectional dimension.
 21. The method according to claim 16, wherein, during the operation of the configuration, wavelengths corresponding to at least one of the at least one first whispering gallery mode resonant frequency or the at least one second whispering gallery mode resonant frequency are within a range of about 1400 nanometers to about 1600 nanometers. 